A new battery supposedly with a charge of 1.5 volts actually has a voltage with a...

 

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A new battery supposedly with a charge of 1.5 volts actually has a voltage with a uniform distribution between 1.43 and 1.60 volts. If a box contains 500 batteries, a) What are the expectation and variance of the number of batteries in the box with a voltage less than 1.5 volts? b) Use the binomial distribution to calculate the probability that at least 140 batteries in the box with a voltage less than 1.5 volts. (Use excel if necessary). c) Also, use the Poisson distribution to make an approximate calculation of the probability that at least 140 batteries in the box with a voltage less than 1.5 volts. A new battery supposedly with a charge of 1.5 volts actually has a voltage with a uniform distribution between 1.43 and 1.60 volts. If a box contains 500 batteries, a) What are the expectation and variance of the number of batteries in the box with a voltage less than 1.5 volts? b) Use the binomial distribution to calculate the probability that at least 140 batteries in the box with a voltage less than 1.5 volts. (Use excel if necessary). c) Also, use the Poisson distribution to make an approximate calculation of the probability that at least 140 batteries in the box with a voltage less than 1.5 volts.